Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
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Σελίδα
... given before his time ; or , finally , whether part of the work may not be ascribed to Theon of Alexandria , who lived in the fourth century of our era . All these opinions have been advanced ; but Dr. Robert Simson , who was ...
... given before his time ; or , finally , whether part of the work may not be ascribed to Theon of Alexandria , who lived in the fourth century of our era . All these opinions have been advanced ; but Dr. Robert Simson , who was ...
Σελίδα
... given after the geometrical demon- stration of each proposition : those propositions which relate to compound proportion are investigated by algebraic pro- cesses only . The first proposition of the sixth book is that which enters into ...
... given after the geometrical demon- stration of each proposition : those propositions which relate to compound proportion are investigated by algebraic pro- cesses only . The first proposition of the sixth book is that which enters into ...
Σελίδα
... given , however , in addition , a demonstration of that proposition in conformity to the tenth definition above - men- tioned . The thirty - third proposition of the sixth book is also demonstrated according to the manner of Euclid ...
... given , however , in addition , a demonstration of that proposition in conformity to the tenth definition above - men- tioned . The thirty - third proposition of the sixth book is also demonstrated according to the manner of Euclid ...
Σελίδα 6
... given by Pythagoras ( a monad in position ) , and which is still defective , since we have no idea of position , except as a part of space , which is , or may be , occupied by magnitude . Euclid's definition of a straight line , that ...
... given by Pythagoras ( a monad in position ) , and which is still defective , since we have no idea of position , except as a part of space , which is , or may be , occupied by magnitude . Euclid's definition of a straight line , that ...
Σελίδα 7
... given a demonstration of it in five theorems . This change of a postulate into an axiom , which cannot be said to carry in itself the evidence of its truth , and which therefore does not possess a character essential to all axioms ...
... given a demonstration of it in five theorems . This change of a postulate into an axiom , which cannot be said to carry in itself the evidence of its truth , and which therefore does not possess a character essential to all axioms ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.
Σελίδα 12 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Σελίδα 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.
Σελίδα 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.
Σελίδα 142 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base
Σελίδα 53 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 30 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 9 - If two triangles have two sides of the one equal to two sides of the...